Bring a large pot of salted water to a boil. Add the tortellini and cook as the label directs. Reserve 1/2 cup cooking water, then drain the pasta.
Meanwhile, heat the butter in a skillet over medium-high heat. Add the shallot and cook, stirring, until slightly soft, about 2 minutes. Add the pumpkin and nutmeg, cook, stirring, 1 minute.
Stir in the cream and bring to a low boil. Reduce the heat to medium low; simmer, stirring, until slightly thickened, about 5 minutes. Stir in the cheese and cook until thick, about 1 more minute. Season with salt and pepper.
Add the tortellini to the skillet and toss with the sauce, adding some of the reserved cooking water to loosen, if needed.
Divide among bowls and top with more cheese and parsley.